A modification of Adomianʹs solution for nonlinear oscillatory systems

In this paper, we consider nonlinear oscillatory equations of the form , whose solutions can be obtained by the decomposition method. But these solutions do not exhibit periodicity, which is characteristic of oscillatory systems. We use an alternative technique by which the solution obtained by the decomposition method is made periodic. The method is described and illustrated with examples. There is no smallness assumption on the parameter occuring in the equation.